# Lecture 4 Part 5 Integrals Class 12 Maths

INTEGRATION OF ALGEBRAIC FUNCTIONS

THIRD METHOD

We apply the third method only if the first two methods are failed.
$px+q=A(ax^2+bx+c)^\prime+B$
It can be applied if the question is in $\int\frac{px+q}{ax^2+bx+c}dx$,$\int\frac{px+q}{\sqrt{ax^2+bx+c}}dx$,$\int (px+q)\sqrt{ax^2+bx+c}dx$.

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Questions discussed in this video:

20. $\int \frac{x+2}{2x^2+6x+5}dx$

21. $\int \frac{x+3}{5-4x-x^2}dx$

22. $\int \frac{5x+3}{\sqrt{x^2+4x+10}}dx$

23. $\int \frac{6x+7}{\sqrt{(x-5)(x-4)}}$

24. $\int (3x-2)\sqrt{x^2+x+1}dx$

25. $\int(x-5)\sqrt{x^2+x}dx$